The spurious components of a system could be generated by different system components. Can you share screenshots of the output with the spurious components you are seeing as well as relevant portions of your schematic? This would help us understand the problem better and give us an idea how we can isolate it. What frequency are you operating in? On Page 16 of the datasheet, figure 22 shows the output noise generated by the DAC for an input code of 800 at 0.1 to 10Hz.